Theorems · Theorem · complex analysis
Complex.abs_im_le_norm
∀ (z : ℂ), |z.im| ≤ ‖z‖
- Defined in
- Mathlib.Analysis.Complex.Norm
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Norm.normstatement · cited by 5,413
- absstatement · cited by 1,814
- Complex.reproof · cited by 882
- Complex.imstatement and proof · cited by 591
- sqproof · cited by 280
- sq_nonnegproof · cited by 106
- le_add_of_nonneg_leftproof · cited by 37
- Complex.normSq_applyproof · cited by 8
- Real.abs_le_sqrtproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- UpperHalfPlane.im_pos_of_dist_center_leproof · cited by 3
- Complex.isCauSeq_improof · cited by 3
- UpperHalfPlane.dist_log_im_leproof · cited by 1
- Complex.abs_im_eq_normproof · cited by 0
- Complex.isBigO_im_sub_improof · cited by 0
- Complex.im_le_normproof · cited by 0